Question

Find the next four terms of each arithmetic sequence.

$\frac{18}{5},\frac{16}{5},\frac{14}{5},\mathrm{...}$

Short answer

The next four terms of the arithmetic sequence are$\frac{12}{5},2,\frac{8}{5},\frac{6}{5}$ .

Step-by-step solution

Step 1. Given Information.

The given arithmetic sequence is$\frac{18}{5},\frac{16}{5},\frac{14}{5},\mathrm{...}$

Step 2. Calculation.

A sequence is said to be arithmetic when the difference between the consecutive terms is always the same.

Here the difference between the first two terms is $\frac{16}{5}-\frac{18}{5}=-\frac{2}{5}$

The difference between the next two terms is $\frac{14}{5}-\frac{16}{5}=-\frac{2}{5}$

So, the common difference is $-\frac{2}{5}$

The next term in the arithmetic sequence is $\frac{14}{5}-\frac{2}{5}=\frac{12}{5}$

The next term in the arithmetic sequence is $\frac{12}{5}-\frac{2}{5}=\frac{10}{5}=2$

The next term in the arithmetic sequence is $2-\frac{2}{5}=\frac{8}{5}$.

The next term in the arithmetic sequence is $\frac{8}{5}-\frac{2}{5}=\frac{6}{5}$.

Step 3. Conclusion.

Hence, the next four terms of the arithmetic sequence are $\frac{12}{5},2,\frac{8}{5},\frac{6}{5}$.